Due to electro negativity difference between B (E.N. = \(2.0)\) and \(\mathrm{Cl}(\mathrm{E} . \mathrm{N} .=3.0)\), the \(\mathrm{B}-\mathrm{Cl}\) bond is polar and hence has a finite dipole moment. The overall dipole moment of a molecule, however, depends upon its geometry. Now \(\mathrm{BCl}_3\) is a planar molecule in which the three \(\mathrm{B}-\mathrm{Cl}\) bonds are inclined at an angle of \(120^{\circ}\). Therefore, the resultant of two \(\mathrm{B}-\mathrm{Cl}\) bonds is cancelled by equal and opposite dipole moment of the third \(\mathrm{B}-\mathrm{Cl}\) bond as shown below:


As a result, overall dipole moment of \(\mathrm{BCl}_3\) is zero.